Multi-product Supply Chain Network Design Research Articles

A new Lagrangian-Benders approach for a concave cost supply chain network design problem

This article presents an extended facility location model for multiproduct supply chain network design, that accounts for concave capacity, transportation, and inventory costs (induced by economies of scale, quantity discounts and risk pooling, respectively). The problem is formulated as a mixed-integer nonlinear program (MINLP) with linear constraints and a large number of separable concave terms in the objective function. We propose a solution approach that combines stabilized Lagrangian relaxation with a novel Benders decomposition. Lagrangian relaxation is used first to decompose the problem by potential warehouse location into low-rank concave minimization subproblems. Benders decomposition is then applied to solve the subproblems by shifting the concave terms to a low-dimensional master problem that is solved effectively through implicit enumeration. Finally, a feasible solution for the original problem is constructed from the partial subproblems solutions by solving a restricted set covering problem. The proposed approach is tested on several instances from the literature and compared against a state-of-the-art solver. Furthermore, a realistic case study is used to demonstrate the impact of concavities in the cost components with extensive sensitivity analyses.

Multi-Period Multi-Product Supply Chain Network Design in the Competitive Environment

This paper studies a supply chain network design model with price competition. The supply chain provides multiple products for a market area in multiple periods. The model considers the location of manufacturers and retailers and assumes a probabilistic customer behavior based on an attraction function depending on both the location and the quality of the retailers. We aim to design the supply chain under the capacity constraint and maximize the supply chain profit in the competitive environment. The problem is formulated as a mixed integer nonlinear programming model. To solve the problem, we propose two heuristic algorithms—Simulated Annealing Search (SA) and Particle Swarm Optimization (PSO)—and numerically demonstrate the effectiveness of the proposed algorithms. Through the sensitivity analysis, we give some management insights.

Integration of multi-product supply chain network design and assembly line balancing

In the supply chain design problems, optimization is usually done without any attention to performance and efficiency of each part of chain. On the other hand, in Assembly Line Balancing (ALB) problems, the objective of the problems is to optimize with regard to the situation of assemblers, while in this set of problems, concentration on some factors such as how to provide raw materials and also sending final products to customers are very important. Since optimal decisions in each problem will affect the other decisions, it is required to study these two matters at the same time; otherwise, the validity of the results will be reduced. In this paper, the problem of integration of multi-product Supply Chain Network designing and ALB are addressed. A Mixed Integer Nonlinear Programming model is proposed to formulate the studied problem. The model is solved by using GAMS in the form of a numerical example given in small size. Finally, Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) as two well-known meta-heuristic algorithms are applied to solve the model with larger dimensions. The computational results show efficiency of the ICA compared with GA. Moreover, after decomposing the integrated mode into two sub problems (ALB problem and Supply Chain Network Design problem), it is shown that optimum cost value of integrated mode is better than total cost functions of two sub-problems separately.

A bi-objective model for a multi-echelon supply chain design considering efficiency and customer satisfaction: a case study in plastic parts industry

One of the fundamental challenges of today’s manufacturing systems is the contradiction between cost efficiency and customer satisfaction. Finding a good balance between good customer satisfaction and supply chain efficiency is a critical problem in the supply chain management. To achieve this goal, a bi-objective mathematical model is suggested in this paper to maximize the efficiency of network and also customer satisfaction. This multi-period and multi-product supply chain network design model consists of suppliers, factories, distribution centers (DCs), and customers. The proposed bi-objective mixed-integer non-linear programming (MINLP) model is a member of the NP-hard class of optimization problems. Hence, two well-known multi-objective metaheuristic algorithms namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Non-dominated Ranked Genetic Algorithm (NRGA) are employed to solve the proposed model. The author uses Taguchi method for tuning the parameters of algorithms in order to achieve better performances. Moreover, a case study in the plastic industry is performed to collect data from the north region of Iran. Some well-known multi-objective metrics such as analysis of variance (ANOVA) is used to measure the performance of the proposed framework. Finally, results demonstrate the efficiency of the proposed framework.

A Three-Echelon Multi-Objective Multi-Period Multi-Product Supply Chain Network Design Problem: A Goal Programming Approach

In this paper, a multi-objective multi-period multi-product supply chain network design problem is introduced. This problem is modeled using a multi-objective mixed integer mathematical programming. The objectives are maximizing the total profit of logistics, maximizing service level, and minimizing inconsistency of operations. Several sets of constraints are considered to handle the real situations of three-echelon supply chains. As the optimum value of conflictive objective functions of the proposed model cannot be met concurrently, so a goal programming approach is used. An illustrative numerical example is provided to show the mechanism of proposed model and the solution procedure. In a numerical example, 1 manufacture, 2 warehouses, 2 distribution centers (DCs), and 2 types of final products are considered in a planning horizon consists of 3 time periods. Products are shipped from the manufacturer to warehouses and then are shipped from the two warehouses to two distribution centers. The distribution centers are the point from which the product are shipped to final consumers. The Model is coded using GAMS software on a Core i7 CPU, using 8GB of RAM with MS-Windows 8.0. The optimum design of supply chain, inventory level for warehouses and distributors, and amount of shipments between echelons are determined.

A large neighborhood search heuristic for supply chain network design

Many exact and approximate solution techniques have been used to solve facility location problems and, more generally, supply chain network design problems. Yet, the Large Neighborhood Search technique (LNS) has almost never been suggested for solving such problems, although it has proven its efficiency and flexibility in solving other complex combinatorial optimization problems. In this paper, we propose an LNS framework for solving a four-layer single period multi-product supply chain network design problem. One important feature of the model is that it includes inter-modality: the itinerary followed by the cargo from origin to destination may take several transportation modes. Moreover, several modes may compete on some arcs. Location decisions for intermediate facilities (e.g. plants and distribution centers) are determined by the LNS while transportation modes and product flow decisions are determined by a greedy heuristic. As a post-optimization step, linear programming is used to optimize product flows once the structure of the logistics network is fixed. Extensive experiments, based on randomly generated instances of different sizes and characteristics, show the effectiveness of the method compared with a state-of-the-art solver.

A priority-based modified encoding–decoding procedure for the design of a bi-objective SC network using meta-heuristic algorithms

This paper aims at a bi-objective optimization of the multi-periodic multi-product supply chain network design (SCND) problem under uncertainty consisting of manufacturing centers, distribution centers, and customer nodes. The problem is considered as a two-stage transportation model while there are several candidate transportation options for each plant. The supposed uncertainty is related to the services of the warehouses and affects the decision making of the SCND that are critical issues. So, the goal is to make the best decisions to maximize the minimum average percentages of products dispatched for each customer in each period while minimizing the sum of strategic, tactical and operational costs. Since the proposed model is of constrained bi-objective mixed-integer nonlinear programming type, we apply a linear programming metric and goal attainment methods to turn the problem into a single-objective model. Each of two methods is separately embedded in simulated annealing, a genetic algorithm, and an imperialist competition algorithm to solve this bi-objective model by MATLAB™ software. Furthermore, we extend a priority-based encoding–decoding method that leads to feasible solutions. The performance of the proposed algorithms is examined on a set of problem instances. Then, some numerical results are provided to demonstrate the algorithm's effectiveness and efficiency further. For this purpose, we propose Duncan's multi-range test and TOPSIS methods.

A highly optimised tolerance-based approach for multi-stage, multi-product supply chain network design

In this paper we propose an algorithm called Highly Optimised Tolerance (HOT) for solving a multi-stage, multi-product supply chain network design problem. HOT is based on power law and control theory. The proposed approach takes its traits from the local incremental algorithm (LIA), which was initially employed to maximise the design parameter (i.e. yield), particularly in the percolation model. The LIA is somewhat analogous to the evolution by natural selection schema. The proposed methodology explores a wide search space and is computationally viable. The HOT algorithm tries to make the system more robust at each step of the optimisation. The objective of this paper is to reduce the total cost of supply chain distribution by selecting the optimum number of facilities in the network. To examine the effectiveness of the HOT algorithm we compare the results with those obtained by applying simulated annealing on a supply chain network design problem with different problem sizes and the same data sets.

A steady-state genetic algorithm for multi-product supply chain network design

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management (SCM). The problem is often an important and strategic operations management problem in SCM. The design task involves the choice of facilities (plants and distribution centers (DCs)) to be opened and the distribution network design to satisfy the customer demand with minimum cost. This paper presents a solution procedure based on steady-state genetic algorithms (ssGA) with a new encoding structure for the design of a single-source, multi-product, multi-stage SCN. The effectiveness of the ssGA has been investigated by comparing its results with those obtained by CPLEX, Lagrangean heuristic, hyrid GA and simulated annealing on a set of SCN design problems with different sizes.